1306.5358 (Rupert L. Frank et al.)

Monotonicity of a relative Rényi entropy    [PDF]

Rupert L. Frank, Elliott H. Lieb

We show that a recent definition of relative R\'enyi entropy is monotone under completely positive, trace preserving maps. This proves a recent conjecture of M\"uller-Lennert et al. The ingredients in our proof are Lieb's concavity theorem, Ando's convexity theorem and theorems of Carlen--Lieb.

View original: http://arxiv.org/abs/1306.5358